Kenyan parents have taken their government to court over the continued imposition of school fees, more than a decade after they were abolished.

The right to free basic education has been enshrined by law in east Africa's biggest economy since 2003. It was expanded to include secondary schools under a new constitution three years ago.

One of the UN's millennium development goals (MDGs) was to increase primary school enrolment by 2015, which would mainly be driven by free basic education. But in Kenya, as in many other sub-Saharan Africa countries, free education has rarely turned out to be exactly that.

The story of Esther Muia, a housekeeper in Nairobi, the capital, is typical of many parents. She earns just £105 a month but has to pay a monthly fee of £42 for each of her three children at secondary school. "We were told [their schooling] was to be free but we are still paying," she said.

Parents of primary schoolchildren are forced to foot the bill for textbooks, uniforms and meals; those at secondary school must pay for tuition.

"Even though it is against the law, schools are charging fees," said Musau Ndunda, head of the Kenyan National Association of Parents, which brought the lawsuit against the education minister, Jacob Kaimenyi, as well as the department's top civil servant, Belio Kipsang. An initial hearing is scheduled for 10 February.

The association's lawyers have cited the country's constitution, which enshrines the right of the child to free basic education, and the 2013 education act, which states that no public school should charge fees. "All we are saying is that the government should implement its own laws," Ndunda said.

For its part, the Kenyan government has asked for a fortnight to respond to the suit. But while parents and officials wrangle over who should shoulder the cost of schooling, experts are wary of repeating past mistakes.

At face value, Kenya's education system has achieved a decade of success. As a result of the introduction of free primary education (FPE) in 2003, enrolment increased from nearly 5 million to almost 9 million. The country is now on track to meet the MDG education target, with 86% of under-11s enrolled in school.

But Ken Ramani, a professor at Mount Kenya University who previously worked at the national examination council, said the FPE initiative had been "a basket of both success and failure". The millions of new schoolchildren have not been matched by new teachers or new classrooms. Average class sizes have shot up from about 40 to 64, meaning that one teacher can sometimes find themselves with a class of up to 100 children.

Soaring attendance has coincided with plummeting results. State schools such as Olympic in Kibera, Nairobi's slum area, which was a top performer 10 years ago, has fallen outside the top 20, with only three children of 500 achieving top marks in maths last year.

"Parents have seen that a lot of schooling doesn't always mean a lot of learning," said Nivi Mukherjee, who runs e-Limu, a private venture that aims to improve standards in Kenyan schools by providing inexpensive tablet computers. "The appalling literacy and numeracy rates can be boiled down to instructional incompetence, a lack of resources and generally poor governance," she added.

Foreign donors such as the UK, which backed FPE, pulled out of direct budget support after a 2009 audit found tens of millions in aid money had disappeared. A Dutch initiative to subsidise textbooks ended in similar disarray.

Kenya spends more than most of its African peers on education, at 17% of the budget, but gets little value for money. "Although many policymakers may not want to admit it," said Mwangi Kimenyi, director of the Africa Growth Initiative, "the truth is that many public schools are literally in a comatose condition."

He points to the rise of private schools, where enrolment tripled from 2005 to 2010, as an indication of failing state schools. State schools have become so bad, he said, that many people do not want to go to them, even when they are free.

Ramani is one of many sceptics who think politicians need to stop making policy promises they cannot keep and focus on reforming the dysfunctional education system. "We are telling people it's free, but secondary education is only subsidised, and the reality is that fees are rising," he said. "We haven't learned anything from the fiasco of free primary education – and it's happening again with secondary schools."